SF II Championship Edition was the best version of Street Fighter, balanced fighters with the ability to use the bosses = EPIC! It was also my personal favorite fighting game 2D or 3D. I bought a snes just for this game even when it was selling for $100.00 (talk about a markup.)
Second is a tie between Tekken 3, and Virtua fighter 3. I just really hated the floaty jumps in Virtua Fighter. Tekken had a good cast but I got tired of the really long combo system.

King of Fighters was a good series too. Most of the SNK fighters got play time from me.

Good point. One thing I love about Street Fighter is group battle. It encourages players to become skilled with more than one character.

I'm not sure. The only fighting games I like arr thr Smash Bros games. I've never really enjoyed playing others and I hate games like WWE and Tekken.

I also have a weakness for weapons-based fighters like SoulCalibur, Samurai Shodown, and The Last Blade. I don't know what it is, but I can't get enough of them.

Ease of button input. SSF IV was a nightmare for me just because of that. A lot of people had an advantage over me because I wasn't fast or accurate enough to execute the most complex moves. Charge moves? Spinning circle moves? Even the less complex moves were impossible for me to input them under pressure. Tekken is a bit more forgiving on the inputs. They are lengthier, but easier to remember and execute.

On top of that, the game needs to be easy to pick up and hard to master. Something that SSF IV isn't. You either became good after losing 300 times or you didn't. You basically get thrown at the wolves if you go online.

Character design is probably the least important to many, but if a game looks too 2D'ish, I'll probably ignore it completely. Alternate costumes and outfits are a must for me. This is why I preferred DOA 5 Ultimate over the rest. Tekken Tag Tournament 2 decided to be extremely lazy with the alternate costumes in quantity and look; they were worse from the much superior Tekken 6.

Story isn't definitely the fighting genre's strength, but many of the games haven't even tried to get a decent story, so it isn't worth choosing a fighting game for the story. Mortal Kombat being an exception for this.

Characters above all other options. Not just favorites. But I need to know most of the characters in the game. Having unknown ones is fine. Like Tatsunoke VS Capcom. I didn't know everyone. The game gets more points for adding in a player I did want in it. MVC 3 added in more Marvel characters I wanted, since game one. So I bought the first release. I bought Soul Calibur II just because of Link. And never bothered after that. With all the bad reviews later ones got.

For me personally, a varied character list and a hefty single player mode. I have really only played one fighting game, due to them being aimed at multiplayer and I have no one to play local with, but I plan to pick up a couple more in the future

I am in the minority but Tekken was and IS by far my favorite fighting game. I even loved TTT2 which most hated. So many different characters to choose from was awesome for me who likes playing a LOT of different characters. A good fighter is in the mechanics and can't just be a button mash fest and you win. A good fighter to me has to be not necessarily easy but accessible. I can't stand the super easy ones because the provide no real depth or challenge in my opinion.

The story is important but doesn't make or rbeak a fighting game for me. I like games with a nice combo system on top of a diverse moveset for characters. It adds more to the mix for me. So the fighiting I playthe most is Tekken, then it WAS Soul Calibur after that followed by SF/MK tied and then was KI followed by all others that I have played over time.

I wil start by saying Tekken. Then if I may add I will say its what i consider the best fighter of them all. Now on to the why and what i consider makes a good fighting game.

• every limb is accurately represented on the face buttons. so regardless of what direction you are facing, a left punch is a left punch and a left grap (with the left hand on top during the grab animation) is a left grab.
• complete 3D movement, so its actually possible to not just jump over attacks, but you can sidestep them, instep them, duck and sway (depending on the character)
• No spam gameplay, contrary to what some may tell you... spamming is near impossible in tekken. unless you are a beginner. Its pretty easy to know and detect moves that can be spammed and punish those that try it. 
• Extremely vast move set, which encourages truly different fighting styles. You can see 5 people that use a specific character and they would all use that chracter differently. Its not about learning the general go to moves of that character and being able to pull them off in a split second.
• tekken is deemed to be combo heavy, its actually not... its punish/set up heavy which usually ends with you doing combos for maximum damage. At its heart tekken is a ground game where both players are fighting for an advantage. Basically, you have to really get into your opponents head to win... or try and overwhelme them with a barrage of uniqe attacks to wear them down and force them into making a mistake. If they are really good you can get punished for this tactic tough.
• evrey character is great, some characters are harder to master than others, but if you can master a character you can beat anyone.
• allows for two distinct fighting styles, agressive and defensive (aka turtle). One has you throwing what seems to be everything at your opponent (but always usually safe moves) and wear them down while the other has you just defending nd trying to counter attack (extremely hard to do cause your defence has to be on point; no easy feat when the average tekken characeter has over 150 different moves)
• just frame moves... this is what seperates the pros from the novices, don't know how to explain this one but if you can pull off a few of these in a fight (which are honest based on normal moves in your arsenal but done to frame perfection or only possible with frame perfection) even if losing that fight you will walk away with the respect of everyone in that room.
• unfortunately, tekken is so deep and vast that its near impossible for most people to get into it. There is no maybe... if you meet someone in tekken that is better than you, you will lose. every single time.

My favorite fighting game to this day is still Soul Calibur 2. Not because of Link being in the GC version, although that helped. The reason it is my favorite is because it has the lengthiest single-player campaign and content I have EVER played in a fighting game, and probably will ever experience.

I've grown stale on fighting games over the last few years. You know why? Because they are feeling more and more like "The Varsity Club," where either you know how to play and get good or you don't. If you're in the latter category, then it feels like they're pretty much saying, "Fuck you then."

I'll take two random examples from fighting games I own and spent a ton of time on: Dead or Alive 2 and Tatsunoko vs. Capcom: both are excellent games, but are pretty bare bones as far as modes go. They have your standard story mode (fight a series of regular matches, then a tough boss at the end, done), your VS. mode, your survival mode, your time attack mode, and your practice. Practice is nice and all, they even tell you how to do moves by pausing the game and showing you your inputs. But they don't actually teach you how to play the game the right way. They don't teach you how to pull off more advanced combos and techniques, either unique to specific characters or important gameplay mechanics. DOA2 can get away with this somewhat, being a little more pick-up-and-play, but TvC is damn near impossible for a noob to enjoy (Dafuq is Baroque?) unless he or she uses a Wiimote, which then becomes a level beyond EZ-mode: "Full-retard mode." So it's convenient that your friends that have never played the game can provide some level of competency using a Wiimote, but it creates two problems (1) they don't learn how to play the right way, and (2) trolls and assholes online would abuse the Wiimote online with Zero, one of the most broken characters known to man.

Getting back to SC2, I love the game because of Weapon Master Mode. It takes the time to teach you everything you need to know beyond knowing, "A button does this, B button does that." It teaches you how, when and why to guard impact, it makes sure you understand the concept of juggling, it even breaches on the idea of frame canceling (lightly). It helped turn me from a button-mashing noob into a serious, competent player who was ready to utilize more techniques than just hoping to get lucky for a throw.

I wish more fighting games would do this. I think it would help expand the fighting game community instead of scaring people away. At the very least, it would give more of us who want to do more than play the same, tired old 20-minute story and time attack modes over and over again, or getting our asses kicked online.